193 lines
6.4 KiB
R
193 lines
6.4 KiB
R
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### R code from vignette source 'validate.Rnw'
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###################################################
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### code chunk number 1: init
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###################################################
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options(continue=" ", width=60)
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options(SweaveHooks=list(fig=function() par(mar=c(4.1, 4.1, .3, 1.1))))
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pdf.options(pointsize=8) #text in graph about the same as regular text
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library(survival, quietly=TRUE)
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###################################################
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### code chunk number 2: breslow1
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###################################################
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breslow1 <- function(beta) {
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# first test data set, Breslow approximation
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r = exp(beta)
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lpl = 2*beta - (log(3*r +3) + 2*log(r+3))
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U = (6+ 3*r - r^2)/((r+1)*(r+3))
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H = r/(r+1)^2 + 6*r/(r+3)^2
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c(beta=beta, loglik=lpl, U=U, H=H)
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}
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beta <- log((3 + sqrt(33))/2)
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temp <- rbind(breslow1(0), breslow1(beta))
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dimnames(temp)[[1]] <- c("beta=0", "beta=solution")
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temp
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###################################################
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### code chunk number 3: validate.Rnw:186-209
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###################################################
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iter <- matrix(0, nrow=6, ncol=4,
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dimnames=list(paste("iter", 0:5),
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c("beta", "loglik", "U", "H")))
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# Exact Newton-Raphson
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beta <- 0
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for (i in 1:5) {
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iter[i,] <- breslow1(beta)
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beta <- beta + iter[i,"U"]/iter[i,"H"]
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}
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print(iter, digits=9)
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# coxph fits
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test1 <- data.frame(time= c(1, 1, 6, 6, 8, 9),
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status=c(1, 0, 1, 1, 0, 1),
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x= c(1, 1, 1, 0, 0, 0))
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temp <- matrix(0, nrow=6, ncol=4,
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dimnames=list(1:6, c("iter", "beta", "loglik", "H")))
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for (i in 0:5) {
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tfit <- coxph(Surv(time, status) ~ x, data=test1,
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ties="breslow", iter.max=i)
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temp[i+1,] <- c(tfit$iter, coef(tfit), tfit$loglik[2], 1/vcov(tfit))
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}
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temp
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###################################################
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### code chunk number 4: mresid1
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###################################################
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mresid1 <- function(r) {
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status <- c(1,0,1,1,0,1)
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xbeta <- c(r,r,r,1,1,1)
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temp1 <- 1/(3*r +3)
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temp2 <- 2/(r+3) + temp1
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status - xbeta*c(temp1, temp1, temp2, temp2, temp2, 1+ temp2)
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}
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r0 <- mresid1(1)
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r1 <- round(mresid1((3 + sqrt(33))/2), 6)
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###################################################
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### code chunk number 5: iter
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###################################################
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temp <- matrix(0, 8, 3)
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dimnames(temp) <- list(paste0("iteration ", 0:7, ':'), c("beta", "loglik", "H"))
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bhat <- 0
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for (i in 1:8) {
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r <- exp(bhat)
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temp[i,] <- c(bhat, 2*(bhat - log(3*r +3)), 2*r/(r+1)^2)
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bhat <- bhat + (r+1)/r
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}
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round(temp,3)
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###################################################
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### code chunk number 6: breslow2
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###################################################
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ufun <- function(r) {
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4 - (r/(r+1) + r/(r+2) + 3*r/(3*r+2) + 6*r/(3*r+1) + 6*r/(3*r+2))
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}
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rhat <- uniroot(ufun, c(.5, 1.5), tol=1e-8)$root
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bhat <- log(rhat)
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c(rhat=rhat, bhat=bhat)
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###################################################
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### code chunk number 7: temp
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###################################################
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true2 <- function(beta, newx=0) {
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r <- exp(beta)
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loglik <- 4*beta - log(r+1) - log(r+2) - 3*log(3*r+2) - 2*log(3*r+1)
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u <- 1/(r+1) + 1/(3*r+1) + 4/(3*r+2) -
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( r/(r+2) +3*r/(3*r+2) + 3*r/(3*r+1))
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imat <- r/(r+1)^2 + 2*r/(r+2)^2 + 6*r/(3*r+2)^2 +
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3*r/(3*r+1)^2 + 3*r/(3*r+1)^2 + 12*r/(3*r+2)^2
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hazard <-c( 1/(r+1), 1/(r+2), 1/(3*r+2), 1/(3*r+1), 1/(3*r+1), 2/(3*r+2) )
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xbar <- c(r/(r+1), r/(r+2), 3*r/(3*r+2), 3*r/(3*r+1), 3*r/(3*r+1),
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3*r/(3*r+2))
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# The matrix of weights, one row per obs, one col per time
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# deaths at 2,3,6,7,8,9
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wtmat <- matrix(c(1,0,0,0,1,0,0,0,0,0,
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0,1,0,1,1,0,0,0,0,0,
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0,0,1,1,1,0,1,1,0,0,
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0,0,0,1,1,0,1,1,0,0,
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0,0,0,0,1,1,1,1,0,0,
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0,0,0,0,0,1,1,1,1,1), ncol=6)
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wtmat <- diag(c(r,1,1,r,1,r,r,r,1,1)) %*% wtmat
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x <- c(1,0,0,1,0,1,1,1,0,0)
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status <- c(1,1,1,1,1,1,1,0,0,0)
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xbar <- colSums(wtmat*x)/ colSums(wtmat)
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n <- length(x)
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# Table of sums for score and Schoenfeld resids
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hazmat <- wtmat %*% diag(hazard) #each subject's hazard over time
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dM <- -hazmat #Expected part
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for (i in 1:6) dM[i,i] <- dM[i,i] +1 #observed
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dM[7,6] <- dM[7,6] +1 # observed
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mart <- rowSums(dM)
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# Table of sums for score and Schoenfeld resids
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# Looks like the last table of appendix E.2.1 of the book
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resid <- dM * outer(x, xbar, '-')
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score <- rowSums(resid)
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scho <- colSums(resid)
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# We need to split the two tied times up, to match coxph
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scho <- c(scho[1:5], scho[6]/2, scho[6]/2)
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var.g <- cumsum(hazard*hazard /c(1,1,1,1,1,2))
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var.d <- cumsum( (xbar-newx)*hazard)
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surv <- exp(-cumsum(hazard) * exp(beta*newx))
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varhaz <- (var.g + var.d^2/imat)* exp(2*beta*newx)
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list(loglik=loglik, u=u, imat=imat, xbar=xbar, haz=hazard,
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mart=mart, score=score, rmat=resid,
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scho=scho, surv=surv, var=varhaz)
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}
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val2 <- true2(bhat)
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rtemp <- round(val2$mart, 6)
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###################################################
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### code chunk number 8: wt1
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###################################################
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ufun <- function(r) {
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xbar <- c( (2*r^2 + 11*r)/(r^2 + 11*r +7), 11*r/(11*r + 5), 2*r/(2*r +1))
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11- (xbar[1] + 10* xbar[2] + 2* xbar[3])
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}
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rhat <- uniroot(ufun, c(1,3), tol= 1e-9)$root
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bhat <- log(rhat)
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c(rhat=rhat, bhat=bhat)
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###################################################
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### code chunk number 9: wt2
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###################################################
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wfun <- function(r) {
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beta <- log(r)
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pl <- 11*beta - (log(r^2 + 11*r + 7) + 10*log(11*r +5) + 2*log(2*r +1))
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xbar <- c((2*r^2 + 11*r)/(r^2 + 11*r +7), 11*r/(11*r +5), 2*r/(2*r +1))
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U <- 11 - (xbar[1] + 10*xbar[2] + 2*xbar[3])
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H <- ((4*r^2 + 11*r)/(r^2 + 11*r +7)- xbar[1]^2) +
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10*(xbar[2] - xbar[2]^2) + 2*(xbar[3]- xbar[3]^2)
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c(loglik=pl, U=U, H=H)
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}
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temp <- matrix(c(wfun(1), wfun(rhat)), ncol=2,
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dimnames=list(c("loglik", "U", "H"), c("beta=0", "beta-hat")))
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round(temp, 6)
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###################################################
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### code chunk number 10: mstate1
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###################################################
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getOption("SweaveHooks")[["fig"]]()
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states <- c("Entry", "a", "b", "c")
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smat <- matrix(0, 4, 4, dimnames=list(states, states))
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smat[1,2:3] <- 1
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smat[2,3] <- smat[3,2] <- smat[3,4] <- smat[2,4] <- 1
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statefig(c(1,2,1), smat)
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